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Abstract

This error correction scheme detects and corrects single and double errors in a data word having n bits, k thereof being information bits and (n-k) check bits. The Bose-Chaudhuri class of codes is applicable.

Country

United States

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English (United States)

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Double Error Correction

This error correction scheme detects and corrects single and double errors
in a data word having n bits, k thereof being information bits and (n-k) check bits.
The Bose-Chaudhuri class of codes is applicable.

From the received data word represented as vector v, the syndrome S is
determined by multiplication of v with the parity-check matrix H which comprises
n rows and (n-k) columns. Syndrome S is thus an (n-k) component vector. If all
syndrome components are zero, the received data vector is error-free. An odd
parity of the syndrome components (odd S-parity) indicates an odd number of
erroneous positions in the data vector, while an even S-parity indicates an even
number. Assuming the received data vector has a maximum of two or less
erroneous positions, an odd S-parity indicates a single error while an even S-
parity indicates a double error.

For single-error correction, syndrome S is compared with the rows of parity-
check matrix H. Assuming the i-th row of matrix H equals S, the i-th position in
the data vector is erroneous and is corrected.

For double-error correction syndrome S is added (= Exclusive OR
in logical algebra) to the different rows of matrix H in subsequent
steps. This logical operation is performed for each component of S
with matrix elements of the same position. Addition of S to the k-th
row of matrix H yields compare vector R(k). This vector R(k) is then
compared with the rows of parity-check matrix H. Assuming the j-...